Discrete Proportional-Integral Control with Constrained Adjustment
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It is well known that discrete feedback control schemes chosen to produce minimum mean square error at the output can require excessive manipulation of the compensating variable. Also very large reductions in the manipulation variance can be obtained at the expense of minor increases in the output variance by using constrained schemes. Unfortunately, however, both the form and the derivation of such schemes are somewhat complicated. The purpose of this article is to show that suitable "tuned" proportional-integral (PI) schemes in which the required adjustment is merely a linear combination of the two last observed errors can do almost as well as the more complicated optimal constrained schemes. If desired, these PI schemes can be applied manually using a feedback adjustment chart which is no more difficult to use than a Shewhart chart. Several examples are given and tables are provided that allow the calculation of the optimal constrained proportional-integral scheme and the resulting adjustment variance and output variance. Methods of tuning such controllers using Evolutionary Operation and experimental design are briefly discussed.